Question

As recently as 1996, the black-footed ferret, North America's only native ferret species, was listed as "extinct in the wild", with only captive individuals surviving in zoos and captive rearing programs. In 2002, 223 ferrets were released in Wyoming in an attempt to re-establish a wild population. Of these only 68 individuals survived the winter into 2003. By 2010, conservation biologists counted 760 ferrets, with an estimated annual growth rate of 0.35, one of the highest of any endangered species managed under the Endangered Species Act. The status of black-footed ferrets will be reevaluated and potentially downgraded from "critically endangered" to "endangered" once their population size exceeds 2000 individuals. Assuming no change to their annual growth rate in 2010, in what calendar year (in AD) would this occur? Answer:

Answer 1

Answer :

• Given : v Population size in 2010, Po= 760. - Growth rate, n= 0.35 per year. • To find: year in which population exceeds 2000. 1. solution: v we know rate of population change dN/dt = r Ng where r= growth rate and N= population size. v Population in any given year will be the sum of population size in previous year + change in population, i.e. - or Pt = Pt-1) + (dN/dt) Pt = PE-1) + r P(t-1) (where N = population in previous yearie Pt-1) v Population in 2014 =(population in 2010) + (change) - (760) + (0.35 X 760) oo P2011 = 1026 similarly, /2012 = (P2011) + (1xP2011) = 1026 + (0.35 x 1026) = 1385 P2013 (1385) + (0.35 x 1385) = 1870 P2014 = (1870) + (0.35x 1870) = 1870 + 654 - 2524

Thus, population will cross a size of 2000 in 2014.